A novel force matrix transformation with optimal load-balance for 3-body potential based parallel molecular dynamics using atom-decomposition in a heterogeneous cluster environment

J. V. Sumanth, David Swanson, Hong Jiang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Evaluating the Force Matrix constitutes the most computationally intensive part of a Molecular Dynamics (MD) simulation. In three-body MD simulations, the total energy of the system is determined by the energy of every unique triple in the system and the force matrix is three-dimensional. The execution time of a three-body MD algorithm is thus proportional to the cube of the number of atoms in the system. Fortunately, there exist symmetries in the Force Matrix that can be exploited to improve the running time of the algorithm. While this optimization is straight forward to implement in the case of sequential code, it has proven to be nontrivial for parallel code even in a homogeneous environment. In this paper, we present a force matrix transformation that is capable of exploiting the symmetries in the force matrix in both a homogeneous and a heterogeneous environment while balancing the load among all the participating processors. The proposed transformation distributes the number oi interactions to be computed uniformly among all the slices of the force matrix along any of the axes. The transformed matrix can be scheduled using any well known heterogeneous slice-level scheduling technique. We also derive theoretical bounds for efficiency and load balance for prior work in the literature. We then prove some interesting and useful properties of our transformation and evaluate its advantages and disadvantages. A loop reordering optimization for the symmetric transformation is described, The performance of an MPI implementation of the transformation is studied in terms of the Step Time Variation Ratio (STVR) in a homogeneous and heterogeneous environment.

Original languageEnglish (US)
Title of host publicationHigh Performance Computing - HiPC 2007 - 14th International Conference, Proceedings
Pages552-565
Number of pages14
StatePublished - Dec 1 2007
Event14th International Conference on High-Performance Computing, HiPC 2007 - Goa, India
Duration: Dec 18 2007Dec 21 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4873 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th International Conference on High-Performance Computing, HiPC 2007
CountryIndia
CityGoa
Period12/18/0712/21/07

Fingerprint

Matrix Transformation
Load Balance
Molecular Dynamics Simulation
Molecular Dynamics
Molecular dynamics
Decomposition
Decompose
Atoms
Heterogeneous Environment
Slice
Symmetry
Dynamic Algorithms
Optimization
Reordering
Energy
Balancing
Computer simulation
Straight
Execution Time
Regular hexahedron

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Sumanth, J. V., Swanson, D., & Jiang, H. (2007). A novel force matrix transformation with optimal load-balance for 3-body potential based parallel molecular dynamics using atom-decomposition in a heterogeneous cluster environment. In High Performance Computing - HiPC 2007 - 14th International Conference, Proceedings (pp. 552-565). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4873 LNCS).

A novel force matrix transformation with optimal load-balance for 3-body potential based parallel molecular dynamics using atom-decomposition in a heterogeneous cluster environment. / Sumanth, J. V.; Swanson, David; Jiang, Hong.

High Performance Computing - HiPC 2007 - 14th International Conference, Proceedings. 2007. p. 552-565 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4873 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sumanth, JV, Swanson, D & Jiang, H 2007, A novel force matrix transformation with optimal load-balance for 3-body potential based parallel molecular dynamics using atom-decomposition in a heterogeneous cluster environment. in High Performance Computing - HiPC 2007 - 14th International Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4873 LNCS, pp. 552-565, 14th International Conference on High-Performance Computing, HiPC 2007, Goa, India, 12/18/07.
Sumanth JV, Swanson D, Jiang H. A novel force matrix transformation with optimal load-balance for 3-body potential based parallel molecular dynamics using atom-decomposition in a heterogeneous cluster environment. In High Performance Computing - HiPC 2007 - 14th International Conference, Proceedings. 2007. p. 552-565. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Sumanth, J. V. ; Swanson, David ; Jiang, Hong. / A novel force matrix transformation with optimal load-balance for 3-body potential based parallel molecular dynamics using atom-decomposition in a heterogeneous cluster environment. High Performance Computing - HiPC 2007 - 14th International Conference, Proceedings. 2007. pp. 552-565 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{a1f018be51554d39b36c77638631ce3f,
title = "A novel force matrix transformation with optimal load-balance for 3-body potential based parallel molecular dynamics using atom-decomposition in a heterogeneous cluster environment",
abstract = "Evaluating the Force Matrix constitutes the most computationally intensive part of a Molecular Dynamics (MD) simulation. In three-body MD simulations, the total energy of the system is determined by the energy of every unique triple in the system and the force matrix is three-dimensional. The execution time of a three-body MD algorithm is thus proportional to the cube of the number of atoms in the system. Fortunately, there exist symmetries in the Force Matrix that can be exploited to improve the running time of the algorithm. While this optimization is straight forward to implement in the case of sequential code, it has proven to be nontrivial for parallel code even in a homogeneous environment. In this paper, we present a force matrix transformation that is capable of exploiting the symmetries in the force matrix in both a homogeneous and a heterogeneous environment while balancing the load among all the participating processors. The proposed transformation distributes the number oi interactions to be computed uniformly among all the slices of the force matrix along any of the axes. The transformed matrix can be scheduled using any well known heterogeneous slice-level scheduling technique. We also derive theoretical bounds for efficiency and load balance for prior work in the literature. We then prove some interesting and useful properties of our transformation and evaluate its advantages and disadvantages. A loop reordering optimization for the symmetric transformation is described, The performance of an MPI implementation of the transformation is studied in terms of the Step Time Variation Ratio (STVR) in a homogeneous and heterogeneous environment.",
author = "Sumanth, {J. V.} and David Swanson and Hong Jiang",
year = "2007",
month = "12",
day = "1",
language = "English (US)",
isbn = "9783540772194",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "552--565",
booktitle = "High Performance Computing - HiPC 2007 - 14th International Conference, Proceedings",

}

TY - GEN

T1 - A novel force matrix transformation with optimal load-balance for 3-body potential based parallel molecular dynamics using atom-decomposition in a heterogeneous cluster environment

AU - Sumanth, J. V.

AU - Swanson, David

AU - Jiang, Hong

PY - 2007/12/1

Y1 - 2007/12/1

N2 - Evaluating the Force Matrix constitutes the most computationally intensive part of a Molecular Dynamics (MD) simulation. In three-body MD simulations, the total energy of the system is determined by the energy of every unique triple in the system and the force matrix is three-dimensional. The execution time of a three-body MD algorithm is thus proportional to the cube of the number of atoms in the system. Fortunately, there exist symmetries in the Force Matrix that can be exploited to improve the running time of the algorithm. While this optimization is straight forward to implement in the case of sequential code, it has proven to be nontrivial for parallel code even in a homogeneous environment. In this paper, we present a force matrix transformation that is capable of exploiting the symmetries in the force matrix in both a homogeneous and a heterogeneous environment while balancing the load among all the participating processors. The proposed transformation distributes the number oi interactions to be computed uniformly among all the slices of the force matrix along any of the axes. The transformed matrix can be scheduled using any well known heterogeneous slice-level scheduling technique. We also derive theoretical bounds for efficiency and load balance for prior work in the literature. We then prove some interesting and useful properties of our transformation and evaluate its advantages and disadvantages. A loop reordering optimization for the symmetric transformation is described, The performance of an MPI implementation of the transformation is studied in terms of the Step Time Variation Ratio (STVR) in a homogeneous and heterogeneous environment.

AB - Evaluating the Force Matrix constitutes the most computationally intensive part of a Molecular Dynamics (MD) simulation. In three-body MD simulations, the total energy of the system is determined by the energy of every unique triple in the system and the force matrix is three-dimensional. The execution time of a three-body MD algorithm is thus proportional to the cube of the number of atoms in the system. Fortunately, there exist symmetries in the Force Matrix that can be exploited to improve the running time of the algorithm. While this optimization is straight forward to implement in the case of sequential code, it has proven to be nontrivial for parallel code even in a homogeneous environment. In this paper, we present a force matrix transformation that is capable of exploiting the symmetries in the force matrix in both a homogeneous and a heterogeneous environment while balancing the load among all the participating processors. The proposed transformation distributes the number oi interactions to be computed uniformly among all the slices of the force matrix along any of the axes. The transformed matrix can be scheduled using any well known heterogeneous slice-level scheduling technique. We also derive theoretical bounds for efficiency and load balance for prior work in the literature. We then prove some interesting and useful properties of our transformation and evaluate its advantages and disadvantages. A loop reordering optimization for the symmetric transformation is described, The performance of an MPI implementation of the transformation is studied in terms of the Step Time Variation Ratio (STVR) in a homogeneous and heterogeneous environment.

UR - http://www.scopus.com/inward/record.url?scp=38349062683&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38349062683&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:38349062683

SN - 9783540772194

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 552

EP - 565

BT - High Performance Computing - HiPC 2007 - 14th International Conference, Proceedings

ER -